Question: The sum of two angles is $74^\circ$. Angle 2 is $141^\circ$ smaller than $4$ times angle 1. What are the measures of the two angles in degrees?
Solution: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 74}$ ${y = 4x-141}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${4x-141}$ for $y$ in the first equation. ${x + }{(4x-141)}{= 74}$ Simplify and solve for $x$ $ x+4x - 141 = 74 $ $ 5x-141 = 74 $ $ 5x = 215 $ $ x = \dfrac{215}{5} $ ${x = 43}$ Now that you know ${x = 43}$ , plug it back into $ {y = 4x-141}$ to find $y$ ${y = 4}{(43)}{ - 141}$ $y = 172 - 141$ ${y = 31}$ You can also plug ${x = 43}$ into $ {x+y = 74}$ and get the same answer for $y$ ${(43)}{ + y = 74}$ ${y = 31}$ The measure of angle 1 is $43^\circ$ and the measure of angle 2 is $31^\circ$.